We demonstrate the existence of the Ince–Gaussian beams that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation. Their transverse structure is described by the Ince polynomials and has an inherent elliptical symmetry. Ince–Gaussian beams constitute the exact and continuous transition modes between Laguerre and Hermite–Gaussian beams. The propagating characteristics are discussed as well.
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